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The idea that there should be an absolute upper limit for the mass of a cold (as distinct from thermal pressure supported) self-gravitating body dates back to the work of Lev Landau, in 1932, whose reasoning was based on the Pauli exclusion principle according to which the Fermionic particles in sufficiently compressed matter would be forced into energy states so high that their rest mass contribution would become negligible compared with the relativistic kinetic contribution determined just by the relevant quantum wavelength λ{\displaystyle \lambda } which would be of the order of the mean interparticle separation. In terms of Planck units with his constant ℏ{\displaystyle \hbar } and the speed of light c{\displaystyle c} and Newton's constant G{\displaystyle G} all set equal to one, there will be a corresponding pressure given roughly by P=1/λ4{\displaystyle P=1/\lambda ^{4}}, that must be balanced by the pressure needed to resist gravity, which for a body of mass M{\displaystyle M} will be given according to the virial theorem roughly by P3=M2ρ4{\displaystyle P^{3}=M^{2}\rho ^{4}}, where ρ{\displaystyle \rho } is the density, which will be given by ρ=m/λ3{\displaystyle \rho =m/\lambda ^{3}} where m{\displaystyle m} is the relevant mass per particle. It can be seen that the wavelength cancels out so that one obtains an approximate mass limit formula of the very simple form

M=1/m2,{\displaystyle M=1/m^{2},}

in which m{\displaystyle m} can be taken to be given roughly by the proton mass, even in the white dwarf case (that of the Chandrasekhar limit) for which the Fermionic particles providing the pressure are electrons, because the mass density is provided by the nuclei in which the neutrons are at most about as numerous as the protons while the latter, for charge neutrality, must be exactly as numerous as the electrons outside.

In a neutron star less massive than the limit, the weight of the star is balanced by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. If its mass is above the limit, the star will collapse to some denser form. It could form a black hole, or change composition and be supported in some other way (for example, by quark degeneracy pressure if it becomes a quark star). Because the properties of hypothetical, more exotic forms of degenerate matter are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.